Angular displacement is usually 01ipw/ zuhywn,rz3ugq3 j 07s express in units of

  Angular velocity is ef a* 9vyo(kmm rnz8ah/u.(:f zxpressed in units of

  Angular acceleration is expliphu i 47 hj3qnd8:p)ressed in units of

  A boy and a girl are ridingb uf); n-ngsh5.iqwtnt 4om 36 on a merry-go-round which is turning at a constant rate. The boy is near the t4 3nbi.n) 5hmtf6w-o;snu gq outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constalg 702p2vn cdtnt rate. The boy is near the outer edge, and the girl is closer to the n2 20 cpl7tdvgcenter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round,4523pheosk ra q7w iy which is turning at a constant rate. The boy is near the outer edge, and the girl is closer 4koir7 5wp h2q3esy,a to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry/rers ; *sllrg)v1rw /-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer t r;* 1s/)glelwsrvr/ ro the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round mp,1bb6lld0z which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the gb1 plbm zl60d,reater tangential acceleration?

  Consider a rigid body that is rotating. Which p7kb6tsp7ecijt1xs. j3q/ 3rof the following is an accurate statemen3 k1 bps.67jp3/cj7 qrt tisext?

  Rolling without slipping5 pe d02+dk e/japmlk6 depends on

  Two equal forces are applied to a door. The first force is apsq6dqfa50,i uplied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendu6is 5a 0qdqf,icular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorojc9psj , ci*3knob. The first force is applied pe*pjs 3cjio,9 crpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firoqt(t3s(7b fd st force is twice as large as the second force. The ratio of the torque ((d 3btfq os7tof the first to the torque of the second is

  What is the quantity used to measure an object's r(flv o4ks/fuc. j4+ciesistance to changes in rotatic+4f(jkv4ofu lcs/. ion?

  Consider two uniform solid sphera2ux* vf25nf28pix lzes where both have the same diameter, but one has twice the mass of the other. The ratio of the lauxifa z82n5fl v2x2p* rger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same ma y(pko0 ym66aiss, but one has twice the radius of the other. The ratio of the larger sphere's moment ofo0 ymy(6pk 6ai inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice /pd+tx9b c d01g+ldco the diameter of the other. The ratio of the largerdp+d9l+x1c gctdo/b0 moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and chzqlyktqi/ 988 .1z o4wwxc/radius R. If these are increased to 2M and 3R, what happens to the sphere's mome1wyxqzhk. 8//qilw 8tcco4z 9nt of inertia about a central axis?

  If a constant net torque is applied to an object, that obje3c 4 (ahgc3yeact will

  The moment of inertia of a solid cylinder about its axi 7ap6ym7) 0wx gqpkas-zzot0,vg5 qr,s is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kin,k-xmrz ozg,0sv q5y0pp g 67w) 7atqaetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of wh6j4.dra9xfq 9poimk)utv e6m z 51u)cich has a mass of 10 kg and a radius of 30 cm. What is tjfqevk51)c96 i9xut zmo46rma pdu. ) he ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls w e4n5s(g;k qq,fb6pcnithout slipping down an inclicb n4fsk(gn pe65q ;,qned plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without sli zolg.9su.7a.u8gusz pping down an inclined plane starting from rest. The angular velocu8ls.ou9 .zg.zsau g7ity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particm .n: i.:/xtr 6uq f)nqmlkv)ales changes when a net external force acts on the system." T.mx))6kq t.:mi fn:r u l/vanqhis statement is

  In what circumstances can the angular velocity of system of paryie b v..;n+0vcnwem+ticles change without any change in the system's angular moe+c;+n.v m.0e wny bivmentum?

  The Earth orbits the Sun in an elliptical orbit. Iu z3 eawzkogb4mb)yg h(u1bb,*p:r/7 gnore any friction which may be present. What happens over tkgepyb)mwa4/( bur1gz oz ubh: 3*b,7ime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun s7 km6eqi;q+4i)nm a k)xmt731 xtxjgin an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting3a1) q; miejk) 76kxtmngmtxi47s +qx speed of the Earth about the Sun?

  An ice skater performs a pirah-jvefoq9e;v,, f 4louette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momej4lfh-o a;fq9,e ev,vntum about the axis of rotation?

  An ice skater performs a pirouette (a fastwt,7v odx5+cs spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the d5c,s+vw t7xo axis of rotation?

  An ice skater performs a pirou54odhp0wt l0iette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the 0 lp4wh05odti axis of rotation?

State the law of conservation of angular momentum6puj0t-vl a(h9z5t v q.

  What arc length doesg/ dq k7szoh,5 the Earth travel in a three month period in its nearly circu kg/ qds5,7ozhlar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m8a.qh;py3/e njeglx;. What distance does the tip of thee .g ha8;qly;/xep3nj second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pywv:bic1g -rap+ifuxa 68v(-zjt 0h1 ;)pxls er minute equivalent to?

  A bicycle wheel rotates uniformtzj) 9(c: 9qhs5 atwgmly through 2.0 revolutions in 4.0 s. What is the frequem awz)gc: t9 qt9j(hs5ncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a f7v htnzws3 ;o jf*cz86requency of 0.40 kHz. The period of its rotation is jo*cwz;t78ns zhv3f6

  A phonograph record rotates at 4r4 wvw9otd .,hgne9j15w tjo;5 rpm. Through what angle does it turn in 0.20 jh nrj5wte1w 499. vow; do,tgs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outera4i )m epbxj4. rim move in 4) amb.xej4p i2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revodmdbqg x2i-b y9.f) f d4p7h szxp-):tlutions in 4.0 s. What is the average angular speed of the whef xs:f7zp9bq id4y).mdd bhg-2pt x- )el?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 jmee.w8r/r-c6 ct lu) b/tm/ms. What is the linear speed of a point 0.10 m from tw cu6.mc/j )tme tm/r8-lreb /he center of the wheel?

  A cable car at a ski resort carries skiers a mt 6w (3dzssurzy09c9s3mlvj/ l o.lv5z6e f.distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pullz9msrvz 0 d/ 33to (lezyw.vs9c56lsfm.u6 j ley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a conr:s)lo r7 h* xsuaz13nstant angular speed of 2.0 rad/s. What is the linear speedrh7 a*urz3x1: lssn)o of a point on the wheel's rim?

  The cutting cord on a gastsr6i jciq2m;e xu 2u9 r7go(1-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the co9( ;6 2 r gmciqsurjixo1e7u2trd?

  A wheel of radius 1.0 m is rotating with a constant an:is5/uoa i+ewgular speed of 2.0 rad/s. Wha:soia5e i u+/wt is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acce) r7g xlejx zt84)px8aleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mo8gl7rexjx )z8a)pxt 4ving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spa l9uj;, ;czqckr)oj1 fce station (r = 1000 m) rotate to produce;jo,lc)qu kc rj;f1 z9 an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve o oi);,aj) g)rqlrybo3f radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) 3 r)jga))oqiyb olr;,is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 x q*s8c 86;hhjd;qkyum with a speed of 20 m/s. The maximum centripetal force (provideky;cx *usqdh 6;88 jqhd by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whirled alnh3w2- nn xz2round in a smooth level table. If the maximum tension that the string can withstand is 250 N, then3z2n l2 -wnhnx what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 c)zwcst +.+igfm rolls without slipping 10 m down a lane at 4.3 m/sw+gz tsf.)+ci .
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a4d.ab )s d m7*two.nom constant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constant angular acpzc 2f93a) cqr;ko n1bceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m r yq1(qx59qm fi hve*l+adius automobile tire rotate after starting from r9v1+qq hyfmi x( qe5l*est and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration of j0,h6yq 9pjkq+maou6z, u.lh : qp;xw1n7 k xu$4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with as 9 nq2)mated; constant angular acceleraet 2ns)9dmq; ation of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an a1mwz (nltv -3q; z.1)sald2u oe6lda-6kb ilangular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the aveqe2l36ti o-mu kwd ) b(nlaa;l1a.1d vsl6zz-rage angular acceleration of the wheel?

  A wheel of diameter of 66vz4u8hu3ln. 0afbhj8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Whvl0fub4 .3hanj86hz u at is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to js5(kcs9 2d1dol dhc4rest over a distance of 115 m. Wha oj d 49ck2c51sldh(dst is the angular acceleration?

  A wheel of diameter of 68.0 cm slows d (w 8zzvvi3i,yown uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wi3z 8vz(v, iywheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed 473 lp*vv*j6fmrswet2o o do 0of 3600 rev/min. When switched off, it rotatesjl*esv 6vf *0p2r47od3 motow 50.0 times at a constant angular acceleration before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require+ xcdt+k6ol rf2yx.l* tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the f+dc.lk fox l2 yrt6+*xorce required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenu/3au4 ea :,jc aoq-sbing to a torque of 90 Nm. If a 30 cm long wrench is used, whaqco, saauebj :-/4au3 t is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine+ ea+z*iupf 6rrtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: maxpv.p idn:6q3b+ 8 upzr64,2 rasxcao ss m is at the origin, mass 2m is at x = a, and, mass 3m is at :aoxpzu6 ,x d2pq ibc rr+3p6s84v.anx = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frict8loc 1it,0tt xionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0x 0l1ot8i, ttc m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionxpi5y /m2 p9azt;r3siless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How manyps9zmr/2; yi5xp i3at radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged ate0ax 0rguic7 r5ts2a) one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is thcesr2a)7tuigax 0 50 re angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be ar9 odx dya906jtrccoa r/gk. ci 1/.-h ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, a/.r. do09jaxr 6 oty1a/cc-gdri9khc ssuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped j) ,b*jtwnx;caround a frictionless disk pulley of mass 7.07 kg xcj;n, )tw jb*and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictcd1pis aq. wtg) 29a8sionless disk pulley of mass 7.07 kg anda c 9wqtd2ipgass18 .) radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to stor5z*mic qt xg.6e $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of inertiau 9pyoja t8r01 z0co2o of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg an38 zabt8kepsv3 3ccj0a6 j+tfd radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the spev p3883tcj+6j 0 b3skaca zfeted of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m ruuhtc:. p+6)( tz365)jyquz a lcqhldolls with a speed of 10 m/s. How high up anut+ 5hlh66)dc tcql: uq. (z)p jzua3y inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released qo+1 .syh;h5 ewy) v-te cmapeam12d( from rest and allowed to roll down an inclined plane. How fast is it moving after o y1h(heem dwcvmp.aq2 ey)as 1-t;+5 dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius c0qu45qg0:mum1dojtt2 - dfpk 9.i.lqp la g- 15 cm rolls without slipping down a 35e incline 1.og0qcj tqt i45. p:adg92m -0mkdl-pulfq uthat is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum changes by*e525 jlkxcvu h 2a-tl $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moms:4v ,scfv ay1ent of inertia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with arms extended has a momkr5dp /w7n:uw,( jwnjent of inertiwwkn7uwjr5d, /: pj (na of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?